Question 1

Use long division to divide. $$\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )$$

Accepted Answer

A)  $x ^ { 2 } + 1$ 
B)  $$x ^ { 2 } + 8 x + 33 - \frac { 129 } { x + 4 }$$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 8 x + 33 + \frac { 120 } { x + 4 }$ 
E)  $x ^ { 2 } + 8 x + 33$ 
A)  $x ^ { 2 } + 1$ 
B)  $$x ^ { 2 } + 8 x + 33 - \frac { 129 } { x + 4 }$$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 8 x + 33 + \frac { 120 } { x + 4 }$ 
E)  $x ^ { 2 } + 8 x + 33$

Question 2

Use synthetic division to divide.​ $\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )$ ​

Accepted Answer

A)  $2 x ^ { 2 } - 3 x - 7 , x \neq 7$ 
B)  $2 x ^ { 2 } - 3 x + 7 , x \neq 7$ 
C)  $3 x ^ { 2 } - 2 x + 7 , x \neq 7$ 
D)  $3 x ^ { 2 } - 2 x - 7 , x \neq 7$ 
E)  $3 x ^ { 2 } + 2 x + 7 , x \neq 7$ 
A)  $2 x ^ { 2 } - 3 x - 7 , x \neq 7$ 
B)  $2 x ^ { 2 } - 3 x + 7 , x \neq 7$ 
C)  $3 x ^ { 2 } - 2 x + 7 , x \neq 7$ 
D)  $3 x ^ { 2 } - 2 x - 7 , x \neq 7$ 
E)  $3 x ^ { 2 } + 2 x + 7 , x \neq 7$

Question 3

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ ,3 
B)  $$( 5 x + 3 ) ^ { 2 } ( x - 3 )$$ x = $- \frac { 3 } { 5 }$ ,3 
C) ​ $( 5 x - 3 ) ( x - 3 ) ^ { 2 };$ x = $\frac { 3 } { 5 }$ ,3 
D)  $( 5 x + 3 ) ( x - 3 ) ^ { 2 };$ x = $- \frac { 3 } { 5 }$ ,3 
E)  $( 5 x - 3 ) ^ { 2 } ( x - 3 );$ x = $\frac { 3 } { 5 }$ ,3 
A)  $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ ,3 
B)  $$( 5 x + 3 ) ^ { 2 } ( x - 3 )$$ x = $- \frac { 3 } { 5 }$ ,3 
C) ​ $( 5 x - 3 ) ( x - 3 ) ^ { 2 };$ x = $\frac { 3 } { 5 }$ ,3 
D)  $( 5 x + 3 ) ( x - 3 ) ^ { 2 };$ x = $- \frac { 3 } { 5 }$ ,3 
E)  $( 5 x - 3 ) ^ { 2 } ( x - 3 );$ x = $\frac { 3 } { 5 }$ ,3

Question 4

Use long division to divide.​ $8 x ^ { 2 } - 67 x - 45 \div x - 9$ ​

Accepted Answer

A) ​ $8 x ^ { 2 } + 5 , x \neq 9$ 
B) ​ $8 x - 5 , x \neq 9$ 
C) ​ $8 x ^ { 2 } - 5 , x \neq 9$ 
D) ​ $8 x + 5 , x \neq 9$ 
E) ​ $8 x + 9 , x \neq 9$ 
A) ​ $8 x ^ { 2 } + 5 , x \neq 9$ 
B) ​ $8 x - 5 , x \neq 9$ 
C) ​ $8 x ^ { 2 } - 5 , x \neq 9$ 
D) ​ $8 x + 5 , x \neq 9$ 
E) ​ $8 x + 9 , x \neq 9$

Question 5

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 113 x ^ { 2 } + 3136$ and determine the multiplicity of each.

Accepted Answer

A) x = 49,multiplicity 2;x = 64,multiplicity 2 
B) x = 7,multiplicity 2;x = 8,multiplicity 2 
C) x = 49,multiplicity 2;x = 8,multiplicity 1 
D) x = -7,multiplicity 2;x = -8,multiplicity 2 
E) x = 7,multiplicity 1;x = -7,multiplicity 1;x = 8,multiplicity 1;x = -8,multiplicity 1 
A) x = 49,multiplicity 2;x = 64,multiplicity 2 
B) x = 7,multiplicity 2;x = 8,multiplicity 2 
C) x = 49,multiplicity 2;x = 8,multiplicity 1 
D) x = -7,multiplicity 2;x = -8,multiplicity 2 
E) x = 7,multiplicity 1;x = -7,multiplicity 1;x = 8,multiplicity 1;x = -8,multiplicity 1

Question 6

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )$

Accepted Answer

A) ​ $3 x ^ { 2 } - 10 x + 8$ 
B) ​ $3 x ^ { 2 } - 7 x + 2$ 
C) ​ $3 x ^ { 2 } + 7 x + 4$ 
D) ​ $3 x ^ { 2 } - 13 x - 3$ 
E) ​ $3 x ^ { 2 } + 5 x - 6$ 
A) ​ $3 x ^ { 2 } - 10 x + 8$ 
B) ​ $3 x ^ { 2 } - 7 x + 2$ 
C) ​ $3 x ^ { 2 } + 7 x + 4$ 
D) ​ $3 x ^ { 2 } - 13 x - 3$ 
E) ​ $3 x ^ { 2 } + 5 x - 6$

Question 7

Use synthetic division to divide.​ $\left( - x ^ { 3 } + 101 x - 825 \right) \div ( x + 11 )$ ​

Accepted Answer

A)  $- x ^ { 2 } + 11 x - 20 , x \neq - 11$ 
B)  $- x ^ { 2 } + 11 x + 20 , x \neq - 11$ 
C)  $x ^ { 2 } + 11 x + 20 , x \neq - 11$ 
D)  $- x ^ { 2 } - 11 x - 20 , x \neq - 11$ 
E)  $x ^ { 2 } + 11 x - 20 , x \neq - 11$ 
A)  $- x ^ { 2 } + 11 x - 20 , x \neq - 11$ 
B)  $- x ^ { 2 } + 11 x + 20 , x \neq - 11$ 
C)  $x ^ { 2 } + 11 x + 20 , x \neq - 11$ 
D)  $- x ^ { 2 } - 11 x - 20 , x \neq - 11$ 
E)  $x ^ { 2 } + 11 x - 20 , x \neq - 11$

Question 8

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ $f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)$ ​

Accepted Answer

A) 3 
B) 4 
C) 2 
D) -1 
E) 0 
A) 3 
B) 4 
C) 2 
D) -1 
E) 0

Question 9

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

Accepted Answer

A) ​x = -4.692 
B) ​x = -8.492,-0.695,1.186 
C) ​x = -3.575 
D) ​x = -4.388,-0.720,1.108 
E) ​x = -3.910,-0.763,1.173 
A) ​x = -4.692 
B) ​x = -8.492,-0.695,1.186 
C) ​x = -3.575 
D) ​x = -4.388,-0.720,1.108 
E) ​x = -3.910,-0.763,1.173

Question 10

If $f ( x ) = - 4 x ^ { 2 } + 6 x - 7$ ,use synthetic division to evaluate f (2).

Accepted Answer

A)  $f ( 2 ) = - 11$ 
B)  $f ( 2 ) = 21$ 
C)  $f ( 2 ) = - 35$ 
D)  $f ( 2 ) = - 3$ 
E)  $f ( 2 ) = - 1$ 
A)  $f ( 2 ) = - 11$ 
B)  $f ( 2 ) = 21$ 
C)  $f ( 2 ) = - 35$ 
D)  $f ( 2 ) = - 3$ 
E)  $f ( 2 ) = - 1$

Question 11

Use long division to divide. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Accepted Answer

A)  $x ^ { 2 } - 4 x + 16$ 
B)  $x ^ { 2 } + 4 x - 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $x ^ { 2 } - 16$ 
E)  $x ^ { 2 } - 16 + \frac { 4 } { x + 4 }$ 
A)  $x ^ { 2 } - 4 x + 16$ 
B)  $x ^ { 2 } + 4 x - 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $x ^ { 2 } - 16$ 
E)  $x ^ { 2 } - 16 + \frac { 4 } { x + 4 }$

Question 12

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25$ .

Accepted Answer

A) x = 1,-5,5,-2 
B) x = -2,-5,-5 
C) x = -1,-5,5, $\frac { 1 } { 2 }$ 
D) ​x = $- \frac { 1 } { 5 }$ , $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ ,5 
E) ​x = -2,-5, $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ 
A) x = 1,-5,5,-2 
B) x = -2,-5,-5 
C) x = -1,-5,5, $\frac { 1 } { 2 }$ 
D) ​x = $- \frac { 1 } { 5 }$ , $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ ,5 
E) ​x = -2,-5, $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$

Question 13

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ $f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )$ ​

Accepted Answer

A) 94 
B) -94 
C) -90 
D) -91 
E) -89 
A) 94 
B) -94 
C) -90 
D) -91 
E) -89

Question 14

Find all rational roots of the equation. ​
13x 3 - 2x 2 + 52x - 8 = 0
​

Accepted Answer

A)  $x = \frac { 2 } { 3 }$ 
B) x = -2i 
C) x = 2i 
D) ​ $x = - \frac { 2 } { 13 }$ 
E) ​ $x = \frac { 2 } { 13 }$ 
A)  $x = \frac { 2 } { 3 }$ 
B) x = -2i 
C) x = 2i 
D) ​ $x = - \frac { 2 } { 13 }$ 
E) ​ $x = \frac { 2 } { 13 }$

Question 15

If x = -4 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( x + 5 ) ( x - 5 ) ( x - 4 ) ; x = - 5,5,4$ 
B)  $( x + 5 ) ^ { 2 } ( x + 4 ) ; x = - 5 , - 4$ 
C)  $( x + 5 ) ( x + 4 ) ^ { 2 } ; x = - 5 , - 4$ 
D)  $( x - 5 ) ( x + 4 ) ( x - 4 ) ; x = 5 , - 4,4$ 
E)  $( x + 5 ) ( x + 4 ) ( x - 4 ) ; x = - 5 , - 4,4$ 
A)  $( x + 5 ) ( x - 5 ) ( x - 4 ) ; x = - 5,5,4$ 
B)  $( x + 5 ) ^ { 2 } ( x + 4 ) ; x = - 5 , - 4$ 
C)  $( x + 5 ) ( x + 4 ) ^ { 2 } ; x = - 5 , - 4$ 
D)  $( x - 5 ) ( x + 4 ) ( x - 4 ) ; x = 5 , - 4,4$ 
E)  $( x + 5 ) ( x + 4 ) ( x - 4 ) ; x = - 5 , - 4,4$

Question 16

Use synthetic division to divide. $\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )$

Accepted Answer

A) ​ $5 x ^ { 2 } + 2 x - 3$ 
B) ​ $5 x ^ { 2 } - 7 x + 12$ 
C)  $5 x ^ { 2 } + 2 x + 5$ 
D)  $5 x ^ { 2 } - 23 x - 15$ 
E)  $5 x ^ { 2 } + x - 4$ 
A) ​ $5 x ^ { 2 } + 2 x - 3$ 
B) ​ $5 x ^ { 2 } - 7 x + 12$ 
C)  $5 x ^ { 2 } + 2 x + 5$ 
D)  $5 x ^ { 2 } - 23 x - 15$ 
E)  $5 x ^ { 2 } + x - 4$

Question 17

Use long division to divide.​ $2 x ^ { 2 } + 14 x + 20 \div x + 5$ ​

Accepted Answer

A)  $2 x - 4 , x \neq - 5$ 
B)  $2 x + 4 , x \neq - 5$ 
C)  $2 x ^ { 2 } - 4 , x \neq - 5$ 
D)  $2 x ^ { 2 } + 4 , x \neq - 5$ 
E)  $2 x ^ { 2 } + 4 x , x \neq - 5$ 
A)  $2 x - 4 , x \neq - 5$ 
B)  $2 x + 4 , x \neq - 5$ 
C)  $2 x ^ { 2 } - 4 , x \neq - 5$ 
D)  $2 x ^ { 2 } + 4 , x \neq - 5$ 
E)  $2 x ^ { 2 } + 4 x , x \neq - 5$

Question 18

Use synthetic division to divide. $\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )$

Accepted Answer

A) ​ $x ^ { 2 } + 3 x - 18$ 
B) ​ $x ^ { 2 } - 3 x - 27$ 
C) ​ $x ^ { 2 } + 9 x + 18$ 
D) ​ $x ^ { 2 } + 9 x - 6$ 
E) ​ $x ^ { 2 } + 6 x + 9$ 
A) ​ $x ^ { 2 } + 3 x - 18$ 
B) ​ $x ^ { 2 } - 3 x - 27$ 
C) ​ $x ^ { 2 } + 9 x + 18$ 
D) ​ $x ^ { 2 } + 9 x - 6$ 
E) ​ $x ^ { 2 } + 6 x + 9$

Question 19

Use long division to divide. ​​ $$\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$$ ​

Accepted Answer

A)  $x ^ { 3 } + 5 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 5 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 1$ 
D)  $x ^ { 2 } + 5 x - 1$ 
E)  $x ^ { 3 } - 5 x ^ { 2 } + 1$ 
A)  $x ^ { 3 } + 5 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 5 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 1$ 
D)  $x ^ { 2 } + 5 x - 1$ 
E)  $x ^ { 3 } - 5 x ^ { 2 } + 1$

Question 20

Use long division to divide.​ $\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )$

Accepted Answer

A)  $- x ^ { 2 } - 7 - \frac { 20 } { x + 2 }$ 
B)  $- x - 3$ 
C)  $- x - 7 - \frac { 10 } { x + 2 }$ 
D) ​ $- x - 10$ 
E) ​ $x + 3$ 
A)  $- x ^ { 2 } - 7 - \frac { 20 } { x + 2 }$ 
B)  $- x - 3$ 
C)  $- x - 7 - \frac { 10 } { x + 2 }$ 
D) ​ $- x - 10$ 
E) ​ $x + 3$

Exam 13: Polynomial and Synthetic Division

Use long division to divide. (x3+4x2+x+4)÷(x+4)\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )(x3+4x2+x+4)÷(x+4)

Use synthetic division to divide.​ (3x3−23x2+21x−49)÷(x−7)\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )(3x3−23x2+21x−49)÷(x−7) ​

If x = 35\frac { 3 } { 5 }53​ is a root of 25x3−105x2+99x−27=025 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 025x3−105x2+99x−27=0 ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use long division to divide.​ 8x2−67x−45÷x−98 x ^ { 2 } - 67 x - 45 \div x - 98x2−67x−45÷x−9 ​

Find all real zeros of the polynomial f(x)=x4−113x2+3136f ( x ) = x ^ { 4 } - 113 x ^ { 2 } + 3136f(x)=x4−113x2+3136 and determine the multiplicity of each.

Use synthetic division to divide. (3x3−19x2+30x−8)÷(x−4)\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )(3x3−19x2+30x−8)÷(x−4)

Use synthetic division to divide.​ (−x3+101x−825)÷(x+11)\left( - x ^ { 3 } + 101 x - 825 \right) \div ( x + 11 )(−x3+101x−825)÷(x+11) ​

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ f(x)=4x3−3x+3,f(12)f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)f(x)=4x3−3x+3,f(21​) ​

Use the zero or root feature of a graphing utility to approximate the zeros of f(x)=2x3+8x2−5x−7f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7f(x)=2x3+8x2−5x−7 accurate to the nearest thousandth.

If f(x)=−4x2+6x−7f ( x ) = - 4 x ^ { 2 } + 6 x - 7f(x)=−4x2+6x−7 ,use synthetic division to evaluate f (2).

Use long division to divide. (x3+64)÷(x+4)\left( x ^ { 3 } + 64 \right) \div ( x + 4 )(x3+64)÷(x+4)

Find all the rational zeros of the function f(x)=−2x4−x3+51x2+25x−25f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25f(x)=−2x4−x3+51x2+25x−25 .

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ f(x)=4x3−3x+8,f(−3)f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )f(x)=4x3−3x+8,f(−3) ​

Find all rational roots of the equation. ​ 13x 3 - 2x 2 + 52x - 8 = 0 ​

If x = -4 is a root of x3+5x2−16x−80=0x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0x3+5x2−16x−80=0 ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use synthetic division to divide. (12+5x3−11x−18x2)÷(x−4)\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )(12+5x3−11x−18x2)÷(x−4)

Use long division to divide.​ 2x2+14x+20÷x+52 x ^ { 2 } + 14 x + 20 \div x + 52x2+14x+20÷x+5 ​

Use synthetic division to divide. (x3−27x+54)÷(x−3)\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )(x3−27x+54)÷(x−3)

Use long division to divide. ​​ (x4+7x3+10x2−x−2)÷(x+2)\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )(x4+7x3+10x2−x−2)÷(x+2) ​

Use long division to divide.​ (−x2−5x−6)÷(x+2)\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )(−x2−5x−6)÷(x+2)

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Use long division to divide. $\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )$

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )$

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use long division to divide. $8 x ^ { 2 } - 67 x - 45 \div x - 9$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 113 x ^ { 2 } + 3136$ and determine the multiplicity of each.

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )$

Use synthetic division to divide. $\left( - x ^ { 3 } + 101 x - 825 \right) \div ( x + 11 )$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)$

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

If $f ( x ) = - 4 x ^ { 2 } + 6 x - 7$ ,use synthetic division to evaluate f (2).

Use long division to divide. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25$ .

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )$

Find all rational roots of the equation. 13x ³ - 2x ² + 52x - 8 = 0

If x = -4 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use synthetic division to divide. $\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )$

Use long division to divide. $2 x ^ { 2 } + 14 x + 20 \div x + 5$

Use synthetic division to divide. $\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )$

Use long division to divide. $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$

Use long division to divide. $\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )$